[Numpy-discussion] Vectorize or rewrite function to work with array inputs?

DParker@chromallo... DParker@chromallo...
Tue Feb 1 14:20:07 CST 2011


I'm not sure I need to dive into cython or C for this - performance is not 
an issue for my problem - I just want a flexible function that will accept 
scalars or arrays. 

Both Sebastian's and eat's suggestions show using indexing to handle the 
conditional statements in the original function. The problem I'm having 
implementing this is in getting the input arguments and outputs to a 
common array size. Here's how I can do this but it seems ugly:

# t and far are function arguments which may be scalars or arrays
# ag is the output array
# need to make everything array with common length
t = np.array(t, ndmin=1)        # Convert t to an array
far = np.array(far, ndmin=1)    # Convert far to an array
ag = t*far*np.nan                       # Make an output array of the 
proper length using broadcasting rules
t = np.zeros_like(ag)+t         # Expand t to the length of the output 
array
far = np.zeros_like(ag)+far     # Expand far to the length of the output 
array

Now with all arrays the same length I can use indexing with logical 
statements:
ag[far<0.005] = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. - 
4.428098e-14 * t ** 4. + \
                1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 2. + 
0.0001684666 * t + 1.368652

The resulting code looks like this:
import numpy as np

def air_gamma_dp(t, far=0.0):
    """
    Specific heat ratio (gamma) of Air/JP8
    t - static temperature, Rankine
    [far] - fuel air ratio [- defaults to 0.0 (dry air)]
    air_gamma - specific heat ratio
    """
    t = np.array(t, ndmin=1)
    far = np.array(far, ndmin=1)
    ag = t*far*np.nan
    t = np.zeros_like(ag)+t
    far = np.zeros_like(ag)+far
 
    far[(far<0.) | (far>0.069)] = np.nan
    t[(t < 379.) | (t > 4731.)] = np.nan
    ag[(far<0.005)] = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. - 
4.428098e-14 * t ** 4. + 
                       1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 2. 
+ 0.0001684666 * t + 1.368652
    t[(t < 699.) | (t > 4731.)] = np.nan
    a6 = 4.114808e-20 * far ** 3. - 1.644588e-20 * far ** 2. + 
3.103507e-21 * far - 3.391308e-22
    a5 = -6.819015e-16 * far ** 3. + 2.773945e-16 * far ** 2. - 
5.469399e-17 * far + 6.058125e-18
    a4 = 4.684637e-12 * far ** 3. - 1.887227e-12 * far ** 2. + 
3.865306e-13 * far - 4.302534e-14
    a3 = -0.00000001700602 * far ** 3. + 0.000000006593809 * far ** 2. - 
0.000000001392629 * far + 1.520583e-10
    a2 = 0.00003431136 * far ** 3. - 0.00001248285 * far ** 2. + 
0.000002688007 * far - 0.0000002651616
    a1 = -0.03792449 * far ** 3. + 0.01261025 * far ** 2. - 0.002676877 * 
far + 0.0001580424
    a0 = 13.65379 * far ** 3. - 3.311225 * far ** 2. + 0.3573201 * far + 
1.372714
    ag[far>=0.005] = a6 * t ** 6. + a5 * t ** 5. + a4 * t ** 4. + a3 * t 
** 3. + a2 * t ** 2. + a1 * t + a0
    return ag

I was hoping there was a more elegant way to do this. 

David Parker 
Chromalloy - TDAG



From:   John Salvatier <jsalvati@u.washington.edu>
To:     Discussion of Numerical Python <numpy-discussion@scipy.org>
Date:   02/01/2011 02:29 PM
Subject:        Re: [Numpy-discussion] Vectorize or rewrite function to 
work with array inputs?
Sent by:        numpy-discussion-bounces@scipy.org



Have you thought about using cython to work with the numpy C-API (
http://wiki.cython.org/tutorials/numpy#UsingtheNumpyCAPI)? This will be 
fast, simple (you can mix and match Python and Cython). 

As for your specific issue: you can simply cast to all the inputs to numpy 
arrays (using asarray 
http://docs.scipy.org/doc/numpy/reference/generated/numpy.asarray.html) to 
deal with scalars. This will make sure they get broadcast correctly.

On Tue, Feb 1, 2011 at 11:22 AM, <DParker@chromalloy.com> wrote:
Thanks for the advice. 

Using Sebastian's advice I was able to write a version that worked when 
the input arguments are both arrays with the same length. The code 
provided by eat works when t is an array, but not for an array of far. 

The numpy.vectorize version works with any combination of scalar or array 
input. I still haven't figured out how to rewrite my function to be as 
flexible as the numpy.vectorize version at accepting either scalars or 
array inputs and properly broadcasting the scalar arguments to the array 
arguments. 

David Parker 
Chromalloy - TDAG 



From:        eat <e.antero.tammi@gmail.com> 
To:        Discussion of Numerical Python <numpy-discussion@scipy.org> 
Date:        01/31/2011 11:37 AM 
Subject:        Re: [Numpy-discussion] Vectorize or rewrite function to 
work with array inputs? 
Sent by:        numpy-discussion-bounces@scipy.org 




Hi,

On Mon, Jan 31, 2011 at 5:15 PM, <DParker@chromalloy.com> wrote: 
I have several functions like the example below that I would like to make 
compatible with array inputs. The problem is the conditional statements 
give a ValueError: The truth value of an array with more than one element 
is ambiguous. Use a.any() or a.all(). I can use numpy.vectorize, but if 
possible I'd prefer to rewrite the function. Does anyone have any advice 
the best way to modify the code to accept array inputs? Thanks in advance 
for any assistance. 
  
If I understod your question correctly, then air_gamma could be coded as: 
def air_gamma_0(t, far=0.0): 
    """ 
    Specific heat ratio (gamma) of Air/JP8 
    t - static temperature, Rankine 
    [far] - fuel air ratio [- defaults to 0.0 (dry air)] 
    air_gamma - specific heat ratio 
    """ 
    if far< 0.: 
        return NAN 
    elif far < 0.005:
        ag= air_gamma_1(t)
        ag[np.logical_or(t< 379., t> 4731.)]= NAN
        return ag
    elif far< 0.069:
        ag= air_gamma_2(t, far)
        ag[np.logical_or(t< 699., t> 4731.)]= NAN
        return ag
    else: 
        return NAN 
Rest of the code is in the attachment. 
  
  
My two cents, 
eat 



NAN = float('nan') 

def air_gamma(t, far=0.0): 
    """ 
    Specific heat ratio (gamma) of Air/JP8 
    t - static temperature, Rankine 
    [far] - fuel air ratio [- defaults to 0.0 (dry air)] 
    air_gamma - specific heat ratio 
    """ 
    if far < 0.: 
        return NAN 
    elif far < 0.005: 
        if t < 379. or t > 4731.: 
            return NAN 
        else: 
            air_gamma = -3.472487e-22 * t ** 6. + 6.218811e-18 * t ** 5. - 
4.428098e-14 * t ** 4. + 1.569889e-10 * t ** 3. - 0.0000002753524 * t ** 
2. + 0.0001684666 * t + 1.368652 
    elif far < 0.069: 
        if t < 699. or t > 4731.: 
            return NAN 
        else: 
            a6 = 4.114808e-20 * far ** 3. - 1.644588e-20 * far ** 2. + 
3.103507e-21 * far - 3.391308e-22 
            a5 = -6.819015e-16 * far ** 3. + 2.773945e-16 * far ** 2. - 
5.469399e-17 * far + 6.058125e-18 
            a4 = 4.684637e-12 * far ** 3. - 1.887227e-12 * far ** 2. + 
3.865306e-13 * far - 4.302534e-14 
            a3 = -0.00000001700602 * far ** 3. + 0.000000006593809 * far 
** 2. - 0.000000001392629 * far + 1.520583e-10 
            a2 = 0.00003431136 * far ** 3. - 0.00001248285 * far ** 2. + 
0.000002688007 * far - 0.0000002651616 
            a1 = -0.03792449 * far ** 3. + 0.01261025 * far ** 2. - 
0.002676877 * far + 0.0001580424 
            a0 = 13.65379 * far ** 3. - 3.311225 * far ** 2. + 0.3573201 * 
far + 1.372714 
            air_gamma = a6 * t ** 6. + a5 * t ** 5. + a4 * t ** 4. + a3 * 
t ** 3. + a2 * t ** 2. + a1 * t + a0 
    elif far >= 0.069: 
        return NAN 
    else: 
        return NAN 
    return air_gamma 

David Parker 
Chromalloy - TDAG
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